New York - Lawyers for the city and about 10,000 rescue and cleanup workers at ground zero have renegotiated a new settlement under which the city’s insurer kicks in more money and the plaintiffs’ lawyers reduce their legal fees to give the workers more money than the original agreement called for.

After nearly three months of renegotiations, the city’s insurer, the WTC Captive Insurance Company, has agreed to increase its payout to plaintiffs to $712.5 million. The previous terms called for payouts totaling $575 million to $657.5 million.

In addition, the plaintiffs’ lawyers have agreed to reduce their fees to a maximum of 25 percent of the settlement amount, down from the 33.33 percent called for in the contingency fee agreements with their clients. As a result, the plaintiffs will get to keep an additional $50 million.

“This settlement ensures guaranteed, immediate and just compensation to the heroic men and women who performed their duties without consideration of the health implications,” said Marc J. Bern, one of the plaintiffs’ lawyers. “Our commitment to our clients has never wavered in the seven years since we took on this litigation and we have done everything within our power, including reducing the fees we agreed to with each of our clients, to achieve the best possible outcome.”

The parties went back to the negotiating table in March after their original settlement was rejected by Judge Alvin K. Hellerstein of United States District Court in Manhattan, who has been overseeing the cases since 2003. The judge said the old agreement did not offer enough compensation to the plaintiffs.

The workers sued the city and its contractors over respiratory illnesses and other injuries they alleged were sustained at the World Trade Center site because they were not given protective equipment or adequate supervision.

The city filed papers with the United States Court of Appeals for the Second Circuit to challenge Judge Hellerstein’s authority to block the settlement, its lawyers also tried to accommodate him to salvage an agreement that has to be accepted by 95 percent of the plaintiffs.

Judge Hellerstein was kept informed of the newly negotiated terms and has indicated that he believes that the modified settlement is “fair and reasonable,” according to a statement released on Thursday by the lawyers.